Group GAP4(128,864)
Name: (C2 . (((C4 x C2) : C2) : C2) = (C4 x C2) . (C4 x C2)) : C2
Maximal quotient:GAP4(64,90)
Real polynomial:
x^128-1280*x^126+790400*x^124-313804800*x^122+90073616640*x^120-199284860672\
00*x^118+3538267363724800*x^116-518251881685760000*x^114+6388917690479421760\
0*x^112-6730141784696437248000*x^110+612983720592768112896000*x^108-48727668\
342775917383680000*x^106+3406469745220700161309184000*x^104-2107388646572892\
29003438080000*x^102+11596897413892692764759598080000*x^100-5701267295473073\
16047336755200000*x^98+25130814326678499618099837874560000*x^96-996253460793\
641502276593482342400000*x^94+35610059047598015273110697522688000000*x^92-11\
50127932262749166181984621109248000000*x^90+33625206758615060320538720043489\
075200000*x^88-891182638564227044820275824194809856000000*x^86+2143715269510\
6902541965179536102103040000000*x^84-468459603688944090773423363879451975680\
000000*x^82+9306535839106904937188560178893200444928000000*x^80-168162469871\
879079732157124402334472355840000000*x^78+2764545932810301856085309518290319\
754076160000000*x^76-41354249915864932324907385548344017751244800000000*x^74\
+562845412292890168044117665897300590770667520000000*x^72-696831572838250786\
5577556694042758208125337600000000*x^70+784442897539066625161575633858489766\
98901299200000000*x^68-80249831306193195088401618847259577384135884800000000\
0*x^66+7455221684711644390211967027935492333670847436800000000*x^64-62838358\
024075343822788506883492628024127225856000000000*x^62+4800430868832443774581\
24342136277078868101840896000000000*x^60-33196916956813212087239924943304763\
80400348037120000000000*x^58+20752676358542314361449422856416382368696924864\
512000000000*x^56-1170924504249198521662022176438541699267198274764800000000\
00*x^54+595252238270143586998213670443900565051368185856000000000000*x^52-27\
21099350299686818335175693467895465013838040268800000000000*x^50+11161493736\
052971840428181078348654676372532764917760000000000*x^48-4098274255448616046\
1113614852814367249525081361612800000000000*x^46+134351210035257967689181381\
330202336648738644131840000000000000*x^44-3920940577640494025908012410622470\
29279350700113920000000000000*x^42+10154688326183127725699630710321648866852\
97345652326400000000000*x^40-23256738758575636910730618037744249603562340019\
07712000000000000*x^38+46919732620150320056495662113248169759702298550599680\
00000000000*x^36-83027616050785293268130657872150254038907851295948800000000\
00000*x^34+12825462517753639391760504737377579101492190288920576000000000000\
*x^32-17201963666032751872629641998240398134667323800289280000000000000*x^30\
+19911514710779162890841956682509237478183690066984960000000000000*x^28-1975\
3482276324931551335817819853274002769925111808000000000000000*x^26+166615988\
71033006267101834516671747468713803870371840000000000000*x^24-11836953582928\
712070047203007011479521190338677964800000000000000*x^22+7003928115056621514\
827934006777120226062830193868800000000000000*x^20-3404881535340484435707228\
624082969294568250408960000000000000000*x^18+1337155352445270044109938556579\
272016568955345305600000000000000*x^16-4152233853915135771264565167003923225\
74239924224000000000000000*x^14+99158909489863148427439788576117181612813189\
120000000000000000*x^12-1754835250560581980607424512406641491092439040000000\
0000000000*x^10+218696092405663761537110582530398720271319040000000000000000\
0*x^8-178404116083839183305236940071098450444288000000000000000000*x^6+85287\
74818975048775422859650178731212800000000000000000000*x^4-199709830032904890\
120215019301634048000000000000000000000*x^2+15916426001386357932029855810523\
13600000000000000000000
Common denominator of the automorphisms:
1906517184928294833715572437125344240697683183746103400170598207047290383640\
4387017271631070713070067973687859888791348441796945792332598124261202761168\
2155730002705894832088731412615868546280373372245690407202654147415692315902\
9211120433697992619505876222643628267950470989462767484182753509939590047911\
6779192703501998162836868352325277091062464648335626141620667538897222207677\
6230085181252171879109359375788010969564015404183078263921319954664922220533\
7512362709290947367148681528587067211563106115985588437337850154989575944057\
0722053383333034559494952316167508615920113508490996072258195842331106891824\
9322010121768195505062592059434197291898001858283928863669993309352795528039\
6208507708548464614127763956242232544944159333986604218834522584997565919595\
3111365815338852234552813072215845934235594395452702720000000000000000000
Complex polynomial:
x^128+1280*x^126+790400*x^124+313804800*x^122+90073616640*x^120+199284860672\
00*x^118+3538267363724800*x^116+518251881685760000*x^114+6388917690479421760\
0*x^112+6730141784696437248000*x^110+612983720592768112896000*x^108+48727668\
342775917383680000*x^106+3406469745220700161309184000*x^104+2107388646572892\
29003438080000*x^102+11596897413892692764759598080000*x^100+5701267295473073\
16047336755200000*x^98+25130814326678499618099837874560000*x^96+996253460793\
641502276593482342400000*x^94+35610059047598015273110697522688000000*x^92+11\
50127932262749166181984621109248000000*x^90+33625206758615060320538720043489\
075200000*x^88+891182638564227044820275824194809856000000*x^86+2143715269510\
6902541965179536102103040000000*x^84+468459603688944090773423363879451975680\
000000*x^82+9306535839106904937188560178893200444928000000*x^80+168162469871\
879079732157124402334472355840000000*x^78+2764545932810301856085309518290319\
754076160000000*x^76+41354249915864932324907385548344017751244800000000*x^74\
+562845412292890168044117665897300590770667520000000*x^72+696831572838250786\
5577556694042758208125337600000000*x^70+784442897539066625161575633858489766\
98901299200000000*x^68+80249831306193195088401618847259577384135884800000000\
0*x^66+7455221684711644390211967027935492333670847436800000000*x^64+62838358\
024075343822788506883492628024127225856000000000*x^62+4800430868832443774581\
24342136277078868101840896000000000*x^60+33196916956813212087239924943304763\
80400348037120000000000*x^58+20752676358542314361449422856416382368696924864\
512000000000*x^56+1170924504249198521662022176438541699267198274764800000000\
00*x^54+595252238270143586998213670443900565051368185856000000000000*x^52+27\
21099350299686818335175693467895465013838040268800000000000*x^50+11161493736\
052971840428181078348654676372532764917760000000000*x^48+4098274255448616046\
1113614852814367249525081361612800000000000*x^46+134351210035257967689181381\
330202336648738644131840000000000000*x^44+3920940577640494025908012410622470\
29279350700113920000000000000*x^42+10154688326183127725699630710321648866852\
97345652326400000000000*x^40+23256738758575636910730618037744249603562340019\
07712000000000000*x^38+46919732620150320056495662113248169759702298550599680\
00000000000*x^36+83027616050785293268130657872150254038907851295948800000000\
00000*x^34+12825462517753639391760504737377579101492190288920576000000000000\
*x^32+17201963666032751872629641998240398134667323800289280000000000000*x^30\
+19911514710779162890841956682509237478183690066984960000000000000*x^28+1975\
3482276324931551335817819853274002769925111808000000000000000*x^26+166615988\
71033006267101834516671747468713803870371840000000000000*x^24+11836953582928\
712070047203007011479521190338677964800000000000000*x^22+7003928115056621514\
827934006777120226062830193868800000000000000*x^20+3404881535340484435707228\
624082969294568250408960000000000000000*x^18+1337155352445270044109938556579\
272016568955345305600000000000000*x^16+4152233853915135771264565167003923225\
74239924224000000000000000*x^14+99158909489863148427439788576117181612813189\
120000000000000000*x^12+1754835250560581980607424512406641491092439040000000\
0000000000*x^10+218696092405663761537110582530398720271319040000000000000000\
0*x^8+178404116083839183305236940071098450444288000000000000000000*x^6+85287\
74818975048775422859650178731212800000000000000000000*x^4+199709830032904890\
120215019301634048000000000000000000000*x^2+15916426001386357932029855810523\
13600000000000000000000
Common denominator of the automorphisms:
1906517184928294833715572437125344240697683183746103400170598207047290383640\
4387017271631070713070067973687859888791348441796945792332598124261202761168\
2155730002705894832088731412615868546280373372245690407202654147415692315902\
9211120433697992619505876222643628267950470989462767484182753509939590047911\
6779192703501998162836868352325277091062464648335626141620667538897222207677\
6230085181252171879109359375788010969564015404183078263921319954664922220533\
7512362709290947367148681528587067211563106115985588437337850154989575944057\
0722053383333034559494952316167508615920113508490996072258195842331106891824\
9322010121768195505062592059434197291898001858283928863669993309352795528039\
6208507708548464614127763956242232544944159333986604218834522584997565919595\
3111365815338852234552813072215845934235594395452702720000000000000000000
Database of Galois polynomials by Bill Allombert and Igor Schein.
Last Modified: Sat, 16 Jun 2018 12:23:16 +0200
Copyleft © 2002-2008 the PARI group.